"Completing the square" for Frobenius norm

Question

Assume $k = <X-W,X-W>_F + <X-Z,X-Z>_F$ is it then possible to write $$argmin_X k = argmin_X norm(X-B)^2_F$$ where $B$ is some function of $W$ and $Z$? Note that F indicates Frobenius inner-product/norm and $X,B,W,Z$ are finite dimensional matrices.

Answer 1

I think the minimizing $X$ is $X = \frac{1}{2}(W+Z)$, so $B = \frac{1}{2}(W+Z)$.